ST2 has an option "Open containing folder..." when you do right-click on source-code screen. On my Ubuntu a stupid Gwenview was opened instead of usual File manager.I removed Gwenview. And now nothing is opened when I choose "Open containing folder...".

How can I connect the option "Open containing folder..." with a file manager on my system so that this file manager will be opened?

Not a Sublime issue. You'll need to pry into KDE config to associate the file manager with an "open directory" intent. The reason Sublime was opening Gwenview is because gwenview has configured KDE to do so, so that when something opens a folder it will open in gwenview.

It seems you're not the only one having this kind of issue, take a look.